The data consists of vegetation % cover by functional group from across CONUS (from AIM, FIA, LANDFIRE, and RAP), as well as climate variables from DayMet, which have been aggregated into mean interannual conditions accross multiple temporal windows.

Dependencies

User defined parameters

print(params)
## $run
## [1] TRUE
## 
## $test_run
## [1] FALSE
## 
## $save_figs
## [1] FALSE
## 
## $ecoregion
## [1] "shrubGrass"
## 
## $response
## [1] "BareGroundCover"
# set to true if want to run for a limited number of rows (i.e. for code testing)
test_run <- params$test_run
save_figs <- params$save_figs
response <- params$response
fit_sample <- TRUE # fit model to a sample of the data
n_train <- 5e4 # sample size of the training data
n_test <- 1e6 # sample size of the testing data (if this is too big the decile dotplot code throws memory errors)


run <- params$run
# set option so resampled dataset created here reproduces earlier runs of this code with dplyr 1.0.10
source("../../../Functions/glmTransformsIterates.R")
source("../../../Functions/transformPreds.R")
source("../../../Functions/StepBeta_mine.R")
#source("src/fig_params.R")
#source("src/modeling_functions.R")
 
library(ggspatial)
library(terra)
library(tidyterra)
library(sf)
library(caret)
library(tidyverse)
library(GGally) # for ggpairs()
library(pdp) # for partial dependence plots
library(gridExtra)
library(knitr)
library(patchwork) # for figure insets etc. 
library(ggtext)
library(StepBeta)
theme_set(theme_classic())
library(here)
library(rsample)
library(kableExtra)
library(glmnet)

read in data

Data compiled in the prepDataForModels.R script

here::i_am("Analysis/VegComposition/ModelFitting/02_ModelFitting.Rmd")
modDat <- readRDS( here("Data_processed", "CoverData", "DataForModels_spatiallyAveraged_withSoils_noSf.rds"))
## there are some values of the annual wet degree days 5th percentile that have -Inf?? change to lowest value for now? 
modDat[is.infinite(modDat$annWetDegDays_5percentile_3yrAnom), "annWetDegDays_5percentile_3yrAnom"] <- -47.8
## same, but for annual water deficit 95th percentile 
modDat[is.infinite(modDat$annWaterDeficit_95percentile_3yrAnom), "annWaterDeficit_95percentile_3yrAnom"] <- -600

# # Convert total cover variables into proportions (for later use in beta regression models) ... proportions are already scaled from zero to 1
# modDat <- modDat %>%
#   mutate(TotalTreeCover = TotalTreeCover/100,
#          CAMCover = CAMCover/100,
#          TotalHerbaceousCover = TotalHerbaceousCover/100,
#          BareGroundCover = BareGroundCover/100,
#          ShrubCover = ShrubCover/100
#          )
# For all response variables, make sure there are no 0s add or subtract .0001 from each, since the Gamma model framework can't handle that
modDat[modDat$TotalTreeCover == 0 & !is.na(modDat$TotalTreeCover), "TotalTreeCover"] <- 0.0001
modDat[modDat$CAMCover == 0 & !is.na(modDat$CAMCover), "CAMCover"] <- 0.0001
modDat[modDat$TotalHerbaceousCover == 0  & !is.na(modDat$TotalHerbaceousCover), "TotalHerbaceousCover"] <- 0.0001
modDat[modDat$BareGroundCover == 0 & !is.na(modDat$BareGroundCover), "BareGroundCover"] <- 0.0001
modDat[modDat$ShrubCover == 0 & !is.na(modDat$ShrubCover), "ShrubCover"] <- 0.0001
modDat[modDat$BroadleavedTreeCover_prop == 0 & !is.na(modDat$BroadleavedTreeCover_prop), "BroadleavedTreeCover_prop"] <- 0.0001
modDat[modDat$NeedleLeavedTreeCover_prop == 0 & !is.na(modDat$NeedleLeavedTreeCover_prop), "NeedleLeavedTreeCover_prop"] <- 0.0001
modDat[modDat$C4Cover_prop == 0 & !is.na(modDat$C4Cover_prop), "C4Cover_prop"] <- 0.0001
modDat[modDat$C3Cover_prop == 0 & !is.na(modDat$C3Cover_prop), "C3Cover_prop"] <- 0.0001
modDat[modDat$ForbCover_prop == 0 & !is.na(modDat$ForbCover_prop), "ForbCover_prop"] <- 0.0001
# 
# modDat[modDat$TotalTreeCover ==1& !is.na(modDat$TotalTreeCover), "TotalTreeCover"] <- 0.999
# modDat[modDat$CAMCover ==1& !is.na(modDat$CAMCover), "CAMCover"] <- 0.999
# modDat[modDat$TotalHerbaceousCover ==1 & !is.na(modDat$TotalHerbaceousCover), "TotalHerbaceousCover"] <- 0.999
# modDat[modDat$BareGroundCover ==1& !is.na(modDat$BareGroundCover), "BareGroundCover"] <- 0.999
# modDat[modDat$ShrubCover ==1& !is.na(modDat$ShrubCover), "ShrubCover"] <- 0.999
# modDat[modDat$BroadleavedTreeCover_prop ==1& !is.na(modDat$BroadleavedTreeCover_prop), "BroadleavedTreeCover_prop"] <- 0.999
# modDat[modDat$NeedleLeavedTreeCover_prop ==1& !is.na(modDat$NeedleLeavedTreeCover_prop), "NeedleLeavedTreeCover_prop"] <- 0.999
# modDat[modDat$C4Cover_prop ==1& !is.na(modDat$C4Cover_prop), "C4Cover_prop"] <- 0.999
# modDat[modDat$C3Cover_prop ==1& !is.na(modDat$C3Cover_prop), "C3Cover_prop"] <- 0.999
# modDat[modDat$ForbCover_prop ==1& !is.na(modDat$ForbCover_prop), "ForbCover_prop"] <- 0.999

Prep data

set.seed(1234)
modDat_1 <- modDat %>% 
  select(-c(prcp_annTotal:annVPD_min)) %>% 
  # mutate(Lon = st_coordinates(.)[,1], 
  #        Lat = st_coordinates(.)[,2])  %>% 
  # st_drop_geometry() %>% 
  # filter(!is.na(newRegion))
  rename("tmin" = tmin_meanAnnAvg_CLIM, 
     "tmax" = tmax_meanAnnAvg_CLIM, #1
     "tmean" = tmean_meanAnnAvg_CLIM, 
     "prcp" = prcp_meanAnnTotal_CLIM, 
     "t_warm" = T_warmestMonth_meanAnnAvg_CLIM,
     "t_cold" = T_coldestMonth_meanAnnAvg_CLIM, 
     "prcp_wet" = precip_wettestMonth_meanAnnAvg_CLIM,
     "prcp_dry" = precip_driestMonth_meanAnnAvg_CLIM, 
     "prcp_seasonality" = precip_Seasonality_meanAnnAvg_CLIM, #2
     "prcpTempCorr" = PrecipTempCorr_meanAnnAvg_CLIM,  #3
     "abvFreezingMonth" = aboveFreezing_month_meanAnnAvg_CLIM, 
     "isothermality" = isothermality_meanAnnAvg_CLIM, #4
     "annWatDef" = annWaterDeficit_meanAnnAvg_CLIM, 
     "annWetDegDays" = annWetDegDays_meanAnnAvg_CLIM,
     "VPD_mean" = annVPD_mean_meanAnnAvg_CLIM, 
     "VPD_max" = annVPD_max_meanAnnAvg_CLIM, #5
     "VPD_min" = annVPD_min_meanAnnAvg_CLIM, #6
     "VPD_max_95" = annVPD_max_95percentile_CLIM, 
     "annWatDef_95" = annWaterDeficit_95percentile_CLIM, 
     "annWetDegDays_5" = annWetDegDays_5percentile_CLIM, 
     "frostFreeDays_5" = durationFrostFreeDays_5percentile_CLIM, 
     "frostFreeDays" = durationFrostFreeDays_meanAnnAvg_CLIM, 
     "soilDepth" = soilDepth, #7
     "clay" = surfaceClay_perc, 
     "sand" = avgSandPerc_acrossDepth, #8
     "coarse" = avgCoarsePerc_acrossDepth, #9
     "carbon" = avgOrganicCarbonPerc_0_3cm, #10
     "AWHC" = totalAvailableWaterHoldingCapacity,
     ## anomaly variables
     tmean_anom = tmean_meanAnnAvg_3yrAnom, #15
     tmin_anom = tmin_meanAnnAvg_3yrAnom, #16
     tmax_anom = tmax_meanAnnAvg_3yrAnom, #17
    prcp_anom = prcp_meanAnnTotal_3yrAnom, #18
      t_warm_anom = T_warmestMonth_meanAnnAvg_3yrAnom,  #19
     t_cold_anom = T_coldestMonth_meanAnnAvg_3yrAnom, #20
      prcp_wet_anom = precip_wettestMonth_meanAnnAvg_3yrAnom, #21
      precp_dry_anom = precip_driestMonth_meanAnnAvg_3yrAnom,  #22
    prcp_seasonality_anom = precip_Seasonality_meanAnnAvg_3yrAnom, #23 
     prcpTempCorr_anom = PrecipTempCorr_meanAnnAvg_3yrAnom, #24
      aboveFreezingMonth_anom = aboveFreezing_month_meanAnnAvg_3yrAnom, #25  
    isothermality_anom = isothermality_meanAnnAvg_3yrAnom, #26
       annWatDef_anom = annWaterDeficit_meanAnnAvg_3yrAnom, #27
     annWetDegDays_anom = annWetDegDays_meanAnnAvg_3yrAnom,  #28
      VPD_mean_anom = annVPD_mean_meanAnnAvg_3yrAnom, #29
      VPD_min_anom = annVPD_min_meanAnnAvg_3yrAnom,  #30
      VPD_max_anom = annVPD_max_meanAnnAvg_3yrAnom,  #31
     VPD_max_95_anom = annVPD_max_95percentile_3yrAnom, #32
      annWatDef_95_anom = annWaterDeficit_95percentile_3yrAnom, #33 
      annWetDegDays_5_anom = annWetDegDays_5percentile_3yrAnom ,  #34
    frostFreeDays_5_anom = durationFrostFreeDays_5percentile_3yrAnom, #35 
      frostFreeDays_anom = durationFrostFreeDays_meanAnnAvg_3yrAnom #36
  )

# small dataset for if testing the data
if(test_run) {
  modDat_1 <- slice_sample(modDat_1, n = 1e5)
}

Add a constant to the response variable (+1) so that models run…

modDat_1[,response] <- modDat_1[,response]+1

Identify the ecoregion and response variable type to use in this model run

ecoregion <- params$ecoregion
response <- params$response
print(paste0("In this model run, the ecoregion is ", ecoregion," and the response variable is ",response))
## [1] "In this model run, the ecoregion is shrubGrass and the response variable is BareGroundCover"

Subset the data to only include data for the ecoregion of interest

if (ecoregion == "shrubGrass") {
  # select data for the ecoregion of interest
  modDat_1 <- modDat_1 %>%
    filter(newRegion == "dryShrubGrass")
} else if (ecoregion == "forest") {
  # select data for the ecoregion of interest
  modDat_1 <- modDat_1 %>% 
    filter(newRegion %in% c("eastForest", "westForest"))
}

# remove the rows that have no observations for the response variable of interest
modDat_1 <- modDat_1[!is.na(modDat_1[,response]),]

Visualize the response variable

hist(modDat_1[,response], main = paste0("Histogram of ",response),
     xlab = paste0(response))

Visualize the predictor variables

The following are the candidate predictor variables for this ecoregion:

if (ecoregion == "shrubGrass") {
  # select potential predictor variables for the ecoregion of interest
        prednames <-
          c(
"tmean"             , "prcp"                    ,"prcp_seasonality"        ,"prcpTempCorr"          , 
"isothermality"     , "annWatDef"               ,"sand"                    ,"coarse"                , 
"carbon"            , "AWHC"                    ,"tmin_anom"               ,"tmax_anom"             , 
"t_warm_anom"       , "prcp_wet_anom"           ,"precp_dry_anom"          ,"prcp_seasonality_anom" , 
"prcpTempCorr_anom" , "aboveFreezingMonth_anom" ,"isothermality_anom"      ,"annWatDef_anom"        , 
"annWetDegDays_anom", "VPD_mean_anom"           ,"VPD_min_anom"            ,"frostFreeDays_5_anom"   )
  
} else if (ecoregion == "forest") {
  # select potential predictor variables for the ecoregion of interest
  prednames <- 
    c(
"tmean"                 ,"prcp"               , "prcp_dry"                , "prcpTempCorr"      ,     
"isothermality"         ,"annWatDef"          , "clay"                    , "sand"              ,     
"coarse"                ,"carbon"             , "AWHC"                    , "tmin_anom"         ,     
"tmax_anom"             ,"prcp_anom"          , "prcp_wet_anom"           , "precp_dry_anom"    ,     
"prcp_seasonality_anom" ,"prcpTempCorr_anom"  , "aboveFreezingMonth_anom" , "isothermality_anom",     
"annWatDef_anom"        ,"annWetDegDays_anom" , "VPD_mean_anom"           , "VPD_max_95_anom"   ,     
"frostFreeDays_5_anom"   )
}

# subset the data to only include these predictors, and remove any remaining NAs 
modDat_1 <- modDat_1 %>% 
  select(prednames, response, newRegion, Year, Long, Lat, NA_L1NAME, NA_L2NAME) %>% 
  drop_na()

names(prednames) <- prednames
df_pred <- modDat_1[, prednames]
# 
# # print the list of predictor variables
# knitr::kable(format = "html", data.frame("Possible_Predictors" = prednames)
# ) %>%
#   kable_styling(bootstrap_options = c("striped", "hover", "condensed")) 
create_summary <- function(df) {
  df %>% 
    pivot_longer(cols = everything(),
                 names_to = 'variable') %>% 
    group_by(variable) %>% 
    summarise(across(value, .fns = list(mean = ~mean(.x, na.rm = TRUE), min = ~min(.x, na.rm = TRUE), 
                                        median = ~median(.x, na.rm = TRUE), max = ~max(.x, na.rm = TRUE)))) %>% 
    mutate(across(where(is.numeric), round, 4))
}

modDat_1[prednames] %>% 
  create_summary() %>% 
  knitr::kable(caption = 'summaries of possible predictor variables') %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"))
summaries of possible predictor variables
variable value_mean value_min value_median value_max
AWHC 14.4956 0.6319 13.9731 35.1058
VPD_mean_anom -0.0192 -0.3600 -0.0181 0.2407
VPD_min_anom -0.0118 -0.1833 -0.0147 0.1399
aboveFreezingMonth_anom 0.0573 -1.3667 0.0370 2.2143
annWatDef 99.7603 1.5871 88.4319 451.1875
annWatDef_anom -0.0592 -3.9347 -0.0569 1.0000
annWetDegDays_anom 0.0023 -1.6606 0.0036 0.9840
carbon 1.0422 0.0001 0.8311 27.0162
coarse 8.2664 0.0000 5.3412 63.1943
frostFreeDays_5_anom -16.5564 -216.0000 -6.0000 55.8000
isothermality 37.4441 23.2374 37.2051 54.8325
isothermality_anom 0.4823 -6.0230 0.4158 8.9119
prcp 419.5502 90.8317 372.5500 1701.8013
prcpTempCorr 0.0534 -0.7694 0.1110 0.6890
prcpTempCorr_anom 0.0166 -0.6495 0.0191 0.5744
prcp_seasonality 0.9363 0.5255 0.9217 1.7468
prcp_seasonality_anom -0.0139 -0.8313 -0.0062 0.4743
prcp_wet_anom -0.0135 -1.9576 0.0065 0.6958
precp_dry_anom -0.0540 -9.0000 0.2450 1.0000
sand 45.9310 2.5763 45.5376 98.9991
t_warm_anom -0.4433 -6.3974 -0.4573 3.3598
tmax_anom -0.2641 -3.4286 -0.2999 2.3198
tmean 10.5621 -2.2935 9.3125 23.9289
tmin_anom -0.4468 -4.0550 -0.4284 2.4361 
# response_summary <- modDat_1 %>% 
#     dplyr::select(#where(is.numeric), -all_of(pred_vars),
#       matches(response)) %>% 
#     create_summary()
# 
# 
# kable(response_summary, 
#       caption = 'summaries of response variables, calculated using paint') %>%
# kable_styling(bootstrap_options = c("striped", "hover", "condensed"))

Plot predictor vars against each other

set.seed(12011993)
# function for colors
my_fn <- function(data, mapping, method="p", use="pairwise", ...){
  
  # grab data
  x <- eval_data_col(data, mapping$x)
  y <- eval_data_col(data, mapping$y)
  
  # calculate correlation
  corr <- cor(x, y, method=method, use=use)
  
  # calculate colour based on correlation value
  # Here I have set a correlation of minus one to blue, 
  # zero to white, and one to red 
  # Change this to suit: possibly extend to add as an argument of `my_fn`
  colFn <- colorRampPalette(c("red", "white", "blue"), interpolate ='spline')
  fill <- colFn(100)[findInterval(corr, seq(-1, 1, length=100))]
  
  ggally_cor(data = data, mapping = mapping, size = 2.5, stars = FALSE, 
             digits = 2, colour = I("black"),...) + 
    theme_void() +
    theme(panel.background = element_rect(fill=fill))
  
}

if (run == TRUE) {
(corrPlot <- modDat_1 %>% 
  select(prednames) %>% 
  slice_sample(n = 5e4) %>% 
  #select(-matches("_")) %>% 
ggpairs( upper = list(continuous = my_fn, size = .1), lower = list(continuous = GGally::wrap("points", alpha = 0.1, size=0.1)), progress = FALSE))
    base::saveRDS(corrPlot, paste0("../ModelFitting/models/", response, "_",ecoregion, "_corrPlot.rds"))
  
  } else {
    # corrPlot <- readRDS(paste0("../ModelFitting/models/", response, "_",ecoregion, "_corrPlot.rds"))
    # (corrPlot)
    print(c("See previous correlation figures"))
  }

Predictor variables compared to binned response variables

set.seed(12011993)
# vector of name of response variables
vars_response <- response

# longformat dataframes for making boxplots
df_sample_plots <-  modDat_1  %>% 
  slice_sample(n = 5e4) %>% 
   rename(response = all_of(response)) %>% 
  mutate(response = case_when(
    response <= .25 ~ ".25", 
    response > .25 & response <=.5 ~ ".5", 
    response > .5 & response <=.75 ~ ".75", 
    response >= .75  ~ "1", 
  )) %>% 
  select(c(response, prednames)) %>% 
  tidyr::pivot_longer(cols = unname(prednames), 
               names_to = "predictor", 
               values_to = "value"
               )  
 

  ggplot(df_sample_plots, aes_string(x= "response", y = 'value')) +
  geom_boxplot() +
  facet_wrap(~predictor , scales = 'free_y') + 
  ylab("Predictor Variable Values") + 
    xlab(response)

Standardize the predictor variables for the model-fitting process

modDat_1_s <- modDat_1 %>% 
  mutate(across(all_of(prednames), base::scale, .names = "{.col}_s")) 
names(modDat_1_s) <- c(names(modDat_1),
                       paste0(prednames, "_s")
                       )
  
scaleFigDat_1 <- modDat_1_s %>% 
  select(c(Long, Lat, Year, prednames)) %>% 
  pivot_longer(cols = all_of(names(prednames)), 
               names_to = "predNames", 
               values_to = "predValues_unScaled")
scaleFigDat_2 <- modDat_1_s %>% 
  select(c(Long, Lat, Year,paste0(prednames, "_s"))) %>% 
  pivot_longer(cols = all_of(paste0(prednames, "_s")), 
               names_to = "predNames", 
               values_to = "predValues_scaled", 
               names_sep = ) %>% 
  mutate(predNames = str_replace(predNames, pattern = "_s$", replacement = ""))

scaleFigDat_3 <- scaleFigDat_1 %>% 
  left_join(scaleFigDat_2)

ggplot(scaleFigDat_3) + 
  facet_wrap(~predNames, scales = "free") +
  geom_histogram(aes(predValues_unScaled), fill = "lightgrey", col = "darkgrey") + 
  geom_histogram(aes(predValues_scaled), fill = "lightblue", col = "blue") +
  xlab ("predictor variable values") + 
  ggtitle("Comparing the distribution of unscaled (grey) to scaled (blue) predictor variables")

Model Fitting

Visualize the level 2 ecoregions and how they differ across environmental space

## visualize the variation between groups across environmental space
## make data into spatial format
modDat_1_sf <- modDat_1 %>% 
  st_as_sf(coords = c("Long", "Lat"), crs = st_crs("PROJCRS[\"unnamed\",\n    BASEGEOGCRS[\"unknown\",\n        DATUM[\"unknown\",\n            ELLIPSOID[\"Spheroid\",6378137,298.257223563,\n                LENGTHUNIT[\"metre\",1,\n                    ID[\"EPSG\",9001]]]],\n        PRIMEM[\"Greenwich\",0,\n            ANGLEUNIT[\"degree\",0.0174532925199433,\n                ID[\"EPSG\",9122]]]],\n    CONVERSION[\"Lambert Conic Conformal (2SP)\",\n        METHOD[\"Lambert Conic Conformal (2SP)\",\n            ID[\"EPSG\",9802]],\n        PARAMETER[\"Latitude of false origin\",42.5,\n            ANGLEUNIT[\"degree\",0.0174532925199433],\n            ID[\"EPSG\",8821]],\n        PARAMETER[\"Longitude of false origin\",-100,\n            ANGLEUNIT[\"degree\",0.0174532925199433],\n            ID[\"EPSG\",8822]],\n        PARAMETER[\"Latitude of 1st standard parallel\",25,\n            ANGLEUNIT[\"degree\",0.0174532925199433],\n            ID[\"EPSG\",8823]],\n        PARAMETER[\"Latitude of 2nd standard parallel\",60,\n            ANGLEUNIT[\"degree\",0.0174532925199433],\n            ID[\"EPSG\",8824]],\n        PARAMETER[\"Easting at false origin\",0,\n            LENGTHUNIT[\"metre\",1],\n            ID[\"EPSG\",8826]],\n        PARAMETER[\"Northing at false origin\",0,\n            LENGTHUNIT[\"metre\",1],\n            ID[\"EPSG\",8827]]],\n    CS[Cartesian,2],\n        AXIS[\"easting\",east,\n            ORDER[1],\n            LENGTHUNIT[\"metre\",1,\n                ID[\"EPSG\",9001]]],\n        AXIS[\"northing\",north,\n            ORDER[2],\n            LENGTHUNIT[\"metre\",1,\n                ID[\"EPSG\",9001]]]]"))


## do a pca of climate across level 2 ecoregions
pca <- prcomp(modDat_1_s[,paste0(prednames, "_s")])
library(factoextra)
(fviz_pca_ind(pca, habillage = modDat_1_s$NA_L2NAME, label = "none", addEllipses = TRUE, ellipse.level = .95, ggtheme = theme_minimal(), alpha.ind = .1))

if(ecoregion == "shrubGrass") {
  print("We'll combine the 'Mediterranean California' and 'Western Sierra Madre Piedmont' ecoregions (into 'Mediterranean Piedmont'). We'll also combine `Tamaulipas-Texas semiarid plain' and 'South Central semiarid prairies' ecoregions (into (`Semiarid plain and prairies`)" )
  
  modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MEDITERRANEAN CALIFORNIA", "WESTERN SIERRA MADRE PIEDMONT"), "NA_L2NAME"] <- "MEDITERRANEAN PIEDMONT"
  modDat_1[modDat_1$NA_L2NAME %in% c("MEDITERRANEAN CALIFORNIA", "WESTERN SIERRA MADRE PIEDMONT"), "NA_L2NAME"] <- "MEDITERRANEAN PIEDMONT"
  
  modDat_1_s[modDat_1_s$NA_L2NAME %in% c("TAMAULIPAS-TEXAS SEMIARID PLAIN", "SOUTH CENTRAL SEMIARID PRAIRIES"), "NA_L2NAME"] <- "SEMIARID PLAIN AND PRAIRIES"
  modDat_1[modDat_1$NA_L2NAME %in% c("TAMAULIPAS-TEXAS SEMIARID PLAIN", "SOUTH CENTRAL SEMIARID PRAIRIES"), "NA_L2NAME"] <- "SEMIARID PLAIN AND PRAIRIES"
}
## [1] "We'll combine the 'Mediterranean California' and 'Western Sierra Madre Piedmont' ecoregions (into 'Mediterranean Piedmont'). We'll also combine `Tamaulipas-Texas semiarid plain' and 'South Central semiarid prairies' ecoregions (into (`Semiarid plain and prairies`)"
# make a table of n for each region
modDat_1 %>% 
  group_by(NA_L2NAME) %>% 
  dplyr::summarize("Number_Of_Observations" = length(NA_L2NAME)) %>% 
  rename("Level_2_Ecoregion" = NA_L2NAME)%>% 
  kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"))
Level_2_Ecoregion Number_Of_Observations
COLD DESERTS 63161
MEDITERRANEAN PIEDMONT 2606
SEMIARID PLAIN AND PRAIRIES 24685
TEMPERATE PRAIRIES 3045
TEXAS-LOUISIANA COASTAL PLAIN 786
WARM DESERTS 10353
WEST-CENTRAL SEMIARID PRAIRIES 19493

Then, look at the spatial distribution and environmental characteristics of the grouped ecoregions

# download map info for visualization
us_states <- suppressMessages(tigris::states())


cropped_states <- suppressMessages(us_states %>%
  dplyr::filter(NAME!="Hawaii") %>%
  dplyr::filter(NAME!="Alaska") %>%
  dplyr::filter(NAME!="Puerto Rico") %>%
  dplyr::filter(NAME!="American Samoa") %>%
  dplyr::filter(NAME!="Guam") %>%
  dplyr::filter(NAME!="Commonwealth of the Northern Mariana Islands") %>%
  dplyr::filter(NAME!="United States Virgin Islands") %>%

  sf::st_sf() %>%
  sf::st_transform(sf::st_crs(modDat_1_sf))) #%>%
  #sf::st_crop(sf::st_bbox(modDat_1_sf)+c(-1,-1,1,1))

map1 <- ggplot() +
  geom_sf(data=cropped_states,fill='white') +
  geom_sf(data=modDat_1_sf,aes(fill=as.factor(NA_L2NAME)),linewidth=0.5,alpha=0.5) +
  geom_point(data=modDat_1,alpha=0.5, 
             aes(x = Long, y = Lat, color=as.factor(NA_L2NAME))) +
  #scale_fill_okabeito() +
  #scale_color_okabeito() +
 # theme_default() +
  theme(legend.position = 'none') +
  labs(title = "Level 2 Ecoregions as spatial blocks")

hull <- modDat_1_sf %>%
  ungroup() %>%
  group_by(NA_L2NAME) %>%
  slice(chull(tmean, prcp))

plot1<-ggplot(data=modDat_1_sf,aes(x=tmean,y=prcp)) +
  geom_polygon(data = hull, alpha = 0.25,aes(fill=NA_L2NAME) )+
  geom_point(aes(group=NA_L2NAME,color=NA_L2NAME),alpha=0.25) +
  theme_minimal() + xlab("Annual Average T_mean - long-term average") +
  ylab("Annual Average Precip - long-term average") #+
  #scale_color_okabeito() +
  #scale_fill_okabeito()

plot2<-ggplot(data=modDat_1_sf %>%
                pivot_longer(cols=tmean:prcp),
              aes(x=value,group=name)) +
  # geom_polygon(data = hull, alpha = 0.25,aes(fill=fold) )+
  geom_density(aes(group=NA_L2NAME,fill=NA_L2NAME),alpha=0.25) +
  theme_minimal() +
  facet_wrap(~name,scales='free')# +
  #scale_color_okabeito() +
  #scale_fill_okabeito()
 
library(patchwork)
(combo <- (map1+plot1)/plot2)

## Currently, removing data from the “Texas Coastal Plain”, since it’s quite different from other regions and is really messing with model fit

modDat_1 <- modDat_1 %>% 
  filter(NA_L2NAME != "TEXAS-LOUISIANA COASTAL PLAIN")

modDat_1_s <- modDat_1_s %>% 
  filter(NA_L2NAME != "TEXAS-LOUISIANA COASTAL PLAIN")

Fit a global model with all of the data

First, fit a LASSO regression model using the glmnet R package

  • This regression is a Gamma glm with a log link
  • Use cross validation across level 2 ecoregions to tune the lambda parameter in the LASSO model
  • this model is fit to using the scaled weather/climate/soils variables
  • this list of possible predictors includes:
    1. main effects
    2. interactions between all soils variables
    3. interactions between climate and weather variables
    4. transformed main effects (squared, log-transformed (add a uniform integer – 20– to all variables prior to log-transformation), square root-transformed (add a uniform integer – 20– to all variables prior to log-transformation))
## 
## Call:  cv.glmnet(x = X[, 2:ncol(X)], y = y, type.measure = "mse", foldid = my_folds,      keep = TRUE, parallel = TRUE, family = stats::Gamma(link = "log"),      alpha = 1, nlambda = 100, standardize = FALSE) 
## 
## Measure: Mean-Squared Error 
## 
##      Lambda Index Measure    SE Nonzero
## min 0.00483    51   206.5 43.60      93
## 1se 0.04943    26   246.1 53.14      18

Then, fit regular glm models (Gamma glm with a log link), first using the coefficients from the ‘best’ lambda identified in the LASSO model, as then using the coefficients from the ‘1SE’ lambda identified from the LASSO (this is the value of lambda such that the cross validation error is within 1 standard error of the minimum).

## fit w/ the identified coefficients from the 'best' lambda, but using the glm function
  mat_glmnet_best <- as.matrix(bestLambda_coef)
  mat2_glmnet_best <- mat_glmnet_best[mat_glmnet_best[,1] != 0,]
  names(mat2_glmnet_best) <- rownames(mat_glmnet_best)[mat_glmnet_best[,1] != 0]

  if(length(mat2_glmnet_best) == 1) {
    f_glm_bestLambda <- as.formula(paste0(response, "~ 1"))
  } else {
  f_glm_bestLambda <- as.formula(paste0(response, " ~ ", paste0(names( mat2_glmnet_best)[2:length(names( mat2_glmnet_best))], collapse = " + ")))
  }
  

  fit_glm_bestLambda <- glm(data = modDat_1_s
                              , formula = 
  f_glm_bestLambda,
               ,family =  stats::Gamma(link = "log")
    )
  
   ## fit w/ the identified coefficients from the '1se' lambda, but using the glm function
  mat_glmnet_1se <- as.matrix(seLambda_coef)
  mat2_glmnet_1se <- mat_glmnet_1se[mat_glmnet_1se[,1] != 0,]
  names(mat2_glmnet_1se) <- rownames(mat_glmnet_1se)[mat_glmnet_1se[,1] != 0]
  if(length(mat2_glmnet_1se) == 1) {
    f_glm_1se <- as.formula(paste0(response, "~ 1"))
  } else {
  f_glm_1se <- as.formula(paste0(response, " ~ ", paste0(names( mat2_glmnet_1se)[2:length(names( mat2_glmnet_1se))], collapse = " + ")))
  }


  fit_glm_se <- glm(data = modDat_1_s, formula = 
  f_glm_1se,
               ,family =  stats::Gamma(link = "log")
    )

Then, we predict (on the training set) using both of these models (best lambda and 1se lambda)

  ## predict on the test data
  # lasso model predictions with the optimal lambda
  optimal_pred <- predict(fit_glm_bestLambda, newx=X[,2:ncol(X)], type = "response")
  optimal_pred_1se <-  predict(fit_glm_se, newx=X[,2:ncol(X)], type = "response")
    null_fit <- glm(#data = data.frame("y" = y, X[,paste0(prednames, "_s")]), 
      formula = y ~ 1, family = stats::Gamma(link = "log"))
  null_pred <- predict(null_fit, newdata = as.data.frame(X), type = "response"
                       )

  # save data
  fullModOut <- list(
    "modelObject" = fit,
    "nullModelObject" = null_fit,
    "modelPredictions" = data.frame(#ecoRegion_holdout = rep(test_eco,length(y)),
      obs=y,
                    pred_opt=optimal_pred, 
                    pred_opt_se = optimal_pred_1se,
                    pred_null=null_pred#,
                    #pred_nopenalty=nopen_pred
                    ))
  
  
# calculate correlations between null and optimal model 
my_cors <- c(cor(optimal_pred, y),
             cor(optimal_pred_1se, y), 
            cor(null_pred, y)
            )

# calculate mse between null and optimal model 
my_mse <- c(mean((fullModOut$modelPredictions$pred_opt -  y)^2) ,
            mean((fullModOut$modelPredictions$pred_opt_se -  y)^2) ,
            mean((fullModOut$modelPredictions$pred_null - y)^2)#,
            #mean((obs_pred$pred_nopenalty - obs_pred$obs)^2)
            )

ggplot() + 
  geom_point(aes(X[,2], fullModOut$modelPredictions$obs), col = "black", alpha = .1) + 
  geom_point(aes(X[,2], fullModOut$modelPredictions$pred_opt), col = "red", alpha = .1) + ## predictions w/ the CV model
  geom_point(aes(X[,2], fullModOut$modelPredictions$pred_opt_se), col = "green", alpha = .1) + ## predictions w/ the CV model (1se lambda)
  geom_point(aes(X[,2], fullModOut$modelPredictions$pred_null), col = "blue", alpha = .1) + 
  labs(title = "A rough comparison of observed and model-predicted values", 
       subtitle = "black = observed values \n red = predictions from 'best lambda' model \n green = predictions from '1se' lambda model \n blue = predictions from null model") +
  xlab(colnames(X)[2])

  #ylim(c(0,200))

The internal cross-validation process to fit the global LASSO model identified an optimal lambda value (regularization parameter) of r{print(best_lambda)}. The lambda value such that the cross validation error is within 1 standard error of the minimum (“1se lambda”) was `r{print(fit$lambda.1se)}`` . The following coefficients were kept in each model:

# the coefficient matrix from the 'best model' -- find and print those coefficients that aren't 0 in a table
coef_glm_bestLambda <- coef(fit_glm_bestLambda) %>% 
  data.frame() 
coef_glm_bestLambda$coefficientName <- rownames(coef_glm_bestLambda)
names(coef_glm_bestLambda)[1] <- "coefficientValue_bestLambda"
# coefficient matrix from the '1se' model 
coef_glm_1se <- coef(fit_glm_se) %>% 
  data.frame() 
coef_glm_1se$coefficientName <- rownames(coef_glm_1se)
names(coef_glm_1se)[1] <- "coefficientValue_1seLambda"
# add together
coefs <- full_join(coef_glm_bestLambda, coef_glm_1se) %>% 
  select(coefficientName, coefficientValue_bestLambda, coefficientValue_1seLambda)

globModTerms <- coefs[!is.na(coefs$coefficientValue_bestLambda), "coefficientName"]

kable(coefs, col.names = c("Coefficient Name", "Value from best lambda model", "Value from 1se lambda model")
      ) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"))
Coefficient Name Value from best lambda model Value from 1se lambda model
(Intercept) 2.7222430 2.7351905
tmean_s -0.3761802 NA
prcp_s -0.4405459 -0.6327000
prcp_seasonality_s -0.2051843 NA
prcpTempCorr_s 0.1434270 -0.0904884
isothermality_s 0.2004326 0.1383234
annWatDef_s 0.5550265 NA
sand_s -0.0504521 NA
coarse_s -0.1018244 NA
carbon_s -0.2967843 -0.3000559
t_warm_anom_s -0.0368321 -0.0389225
prcp_wet_anom_s 0.0687358 NA
prcp_seasonality_anom_s -0.0584233 NA
prcpTempCorr_anom_s 0.0145293 NA
aboveFreezingMonth_anom_s -0.0045252 NA
isothermality_anom_s -0.0051306 NA
annWatDef_anom_s 0.0181448 -0.0347483
VPD_mean_anom_s -0.0172854 NA
VPD_min_anom_s -0.0089216 NA
I(prcp_s^2) 0.0516081 0.0824279
I(annWatDef_s^2) -0.0367622 NA
I(t_warm_anom_s^2) -0.0055154 NA
I(prcp_wet_anom_s^2) 0.0021877 NA
I(precp_dry_anom_s^2) -0.0079027 -0.0044463
I(aboveFreezingMonth_anom_s^2) -0.0044362 NA
I(isothermality_anom_s^2) -0.0019802 NA
I(annWatDef_anom_s^2) 0.0065186 0.0053459
I(VPD_mean_anom_s^2) 0.0142162 NA
I(sand_s^2) 0.0288301 NA
I(coarse_s^2) 0.0190760 -0.0261743
I(carbon_s^2) 0.0180356 0.0174695
I(AWHC_s^2) 0.0072500 NA
prcp_seasonality_s:aboveFreezingMonth_anom_s 0.0047701 NA
prcp_wet_anom_s:aboveFreezingMonth_anom_s 0.0099563 NA
prcpTempCorr_anom_s:aboveFreezingMonth_anom_s -0.0023548 NA
isothermality_s:annWatDef_anom_s -0.0102505 NA
tmean_s:annWatDef_anom_s -0.0156641 NA
annWatDef_anom_s:VPD_mean_anom_s -0.0182079 NA
isothermality_s:annWatDef_s -0.0925822 -0.0417823
prcpTempCorr_s:annWatDef_s 0.0064852 0.1313229
annWatDef_s:precp_dry_anom_s -0.0180611 NA
annWatDef_s:tmin_anom_s 0.0077981 NA
isothermality_anom_s:annWetDegDays_anom_s -0.0023456 NA
prcp_s:annWetDegDays_anom_s 0.0208036 NA
prcp_wet_anom_s:annWetDegDays_anom_s 0.0091038 NA
t_warm_anom_s:annWetDegDays_anom_s 0.0055791 NA
isothermality_s:frostFreeDays_5_anom_s 0.0258395 NA
prcp_seasonality_s:frostFreeDays_5_anom_s -0.0086098 NA
prcpTempCorr_anom_s:frostFreeDays_5_anom_s 0.0052734 NA
prcpTempCorr_s:frostFreeDays_5_anom_s -0.0098251 NA
t_warm_anom_s:frostFreeDays_5_anom_s 0.0021006 NA
frostFreeDays_5_anom_s:tmax_anom_s -0.0060863 NA
isothermality_s:isothermality_anom_s -0.0196208 NA
prcp_s:isothermality_anom_s -0.0293285 NA
prcp_seasonality_s:isothermality_anom_s 0.0111428 NA
prcpTempCorr_s:isothermality_anom_s 0.0026850 NA
t_warm_anom_s:isothermality_anom_s 0.0102998 NA
prcp_s:isothermality_s -0.0687577 NA
prcp_seasonality_s:isothermality_s -0.0155584 NA
isothermality_s:prcp_wet_anom_s -0.0210486 NA
prcpTempCorr_s:isothermality_s -0.0623664 -0.0134667
isothermality_s:tmax_anom_s -0.0159104 NA
prcp_s:prcp_wet_anom_s -0.0036905 NA
prcp_s:prcpTempCorr_s -0.1511776 -0.0386927
prcp_s:t_warm_anom_s 0.0052132 NA
tmean_s:prcp_s -0.0055695 NA
prcp_s:VPD_mean_anom_s 0.0167623 NA
prcp_seasonality_anom_s:prcpTempCorr_anom_s 0.0043801 NA
prcpTempCorr_s:prcp_seasonality_anom_s -0.0025862 NA
t_warm_anom_s:prcp_seasonality_anom_s -0.0145230 NA
prcp_seasonality_anom_s:VPD_mean_anom_s 0.0156804 NA
prcp_seasonality_s:prcp_wet_anom_s -0.0139963 NA
prcp_seasonality_s:prcpTempCorr_s -0.0476319 NA
tmean_s:prcp_seasonality_s 0.0215243 NA
prcp_seasonality_s:VPD_min_anom_s 0.0101070 NA
prcp_wet_anom_s:tmax_anom_s -0.0093135 NA
tmean_s:prcp_wet_anom_s 0.0237607 NA
prcpTempCorr_s:prcpTempCorr_anom_s 0.0235148 NA
prcpTempCorr_anom_s:precp_dry_anom_s 0.0060827 NA
prcpTempCorr_s:t_warm_anom_s -0.0108711 NA
tmean_s:prcpTempCorr_s 0.1655763 NA
prcpTempCorr_s:tmin_anom_s -0.0206630 NA
prcpTempCorr_s:VPD_mean_anom_s 0.0110829 NA
t_warm_anom_s:VPD_mean_anom_s -0.0103687 NA
tmean_s:tmax_anom_s -0.0083286 NA
tmean_s:VPD_mean_anom_s 0.0040330 NA
tmean_s:VPD_min_anom_s 0.0072932 NA
VPD_min_anom_s:tmin_anom_s 0.0139375 NA
VPD_mean_anom_s:VPD_min_anom_s -0.0305533 NA
carbon_s:AWHC_s -0.0773133 -0.0525625
coarse_s:AWHC_s 0.0388003 NA
sand_s:AWHC_s 0.0272073 NA
coarse_s:carbon_s 0.0159447 NA
sand_s:carbon_s 0.0143053 NA
I(isothermality_s^2) NA -0.0059811
carbon_s:coarse_s NA 0.0419865

Visualizations of Model Predictions and Residuals – using best lambda model

observed vs. predicted values

Predicting on the data

  # create prediction for each each model
# (i.e. for each fire proporation variable)
predict_by_response <- function(mod, df) {
  df_out <- df
  response_name <- paste0(response, "_pred")
  df_out <- df_out %>% cbind(predict(mod, newx= df_out, #s="lambda.min", 
                                     type = "response"))
   colnames(df_out)[ncol(df_out)] <- response_name
  return(df_out)
}

pred_glm1 <- predict_by_response(fit_glm_bestLambda, X[,2:ncol(X)])

# add back in true y values
pred_glm1 <- pred_glm1 %>% 
  cbind( data.frame("y" = y))
# rename the true response column to not be 'y_test' 
colnames(pred_glm1)[which(colnames(pred_glm1) == "y")] <- paste(response)

# add back in lat/long data 
pred_glm1 <- pred_glm1 %>% 
  cbind(modDat_1_s[,c("Long", "Lat", "Year")])

pred_glm1$resid <- pred_glm1[,response] - pred_glm1[,paste0(response, "_pred")]
pred_glm1$extremeResid <- NA
pred_glm1[pred_glm1$resid > 70 | pred_glm1$resid < -70,"extremeResid"] <- 1

# plot(x = pred_glm1[,response],
#      y = pred_glm1[,paste0(response, "_pred")],
#      xlab = "observed values", ylab = "predicted values")
# points(x = pred_glm1[!is.na(pred_glm1$extremeResid), response],
#        y = pred_glm1[!is.na(pred_glm1$extremeResid), paste0(response, "_pred")],
#        col = "red")

Maps of Observations, Predictions, and Residuals=

Observations across the temporal range of the dataset

pred_glm1 <- pred_glm1 %>% 
  mutate(resid = .[[response]] - .[[paste0(response,"_pred")]]) 

# rasterize
# get reference raster
test_rast <-  rast("../../../Data_raw/dayMet/rawMonthlyData/orders/70e0da02b9d2d6e8faa8c97d211f3546/Daymet_Monthly_V4R1/data/daymet_v4_prcp_monttl_na_1980.tif") %>% 
  terra::aggregate(fact = 8, fun = "mean")
## |---------|---------|---------|---------|=========================================                                          
# rasterize data
plotObs <- pred_glm1 %>% 
         drop_na(paste(response)) %>% 
  #slice_sample(n = 5e4) %>%
  terra::vect(geom = c("Long", "Lat")) %>% 
  terra::set.crs(crs(test_rast)) %>% 
  terra::rasterize(y = test_rast, 
                   field = response, 
                   fun = mean) #%>% 
  #terra::aggregate(fact = 2, fun = mean, na.rm = TRUE) %>% 
  #terra::crop(ext(-1950000, 1000000, -1800000, 1000000))

# get the extent of this particular raster, and crop it accordingly
tempExt <- crds(plotObs, na.rm = TRUE)

plotObs_2 <- plotObs %>% 
  crop(ext(min(tempExt[,1]), max(tempExt[,1]),
           min(tempExt[,2]), max(tempExt[,2])) 
       )
# make figures
ggplot() +
geom_spatraster(data = plotObs_2) + 
  geom_sf(data=cropped_states %>% st_transform(crs = st_crs(test_rast)) %>% st_crop(st_bbox(plotObs_2)),fill=NA ) +
labs(title = paste0("Observations of ", response, " in the ",ecoregion, " ecoregion"),
     subtitle = "bestLambda model") +
  scale_fill_gradient2(low = "brown",
                       mid = "wheat" ,
                       high = "darkgreen" , 
                       midpoint = 0,   na.value = "lightgrey")

Predictions across the temporal range of the dataset

# rasterize data
plotPred <- pred_glm1 %>% 
         drop_na(paste0(response,"_pred")) %>% 
  #slice_sample(n = 5e4) %>%
  terra::vect(geom = c("Long", "Lat")) %>% 
  terra::set.crs(crs(test_rast)) %>% 
  terra::rasterize(y = test_rast, 
                   field = paste0(response,"_pred"), 
                   fun = mean) #%>% 
  #terra::aggregate(fact = 2, fun = mean, na.rm = TRUE) %>% 
  #terra::crop(ext(-1950000, 1000000, -1800000, 1000000))

# get the point location of those predictions that are > 100
highPred_points <- pred_glm1 %>% 
  filter(.[[paste0(response,"_pred")]] > 100 | 
           .[[paste0(response, "_pred")]] < 0) %>% 
  terra::vect(geom = c("Long", "Lat")) %>% 
  terra::set.crs(crs(test_rast)) 

# get the extent of this particular raster, and crop it accordingly
tempExt <- crds(plotPred, na.rm = TRUE)

plotPred_2 <- plotPred %>% 
  crop(ext(min(tempExt[,1]), max(tempExt[,1]),
           min(tempExt[,2]), max(tempExt[,2])) 
       )
# make figures
ggplot() +
geom_spatraster(data = plotPred_2) + 
  geom_sf(data=cropped_states %>% st_transform(crs = st_crs(test_rast)) %>% st_crop(st_bbox(plotObs_2)),fill=NA )  + geom_sf(data = highPred_points, col = "red") +
labs(title = paste0("Predictions from the fitted model of ", response, " in the ",ecoregion, " ecoregion"),
     subtitle =  "bestLambda model")  +
  scale_fill_gradient2(low = "wheat",
                       mid = "darkgreen",
                       high = "red" , 
                       midpoint = 100,   na.value = "lightgrey",
                       limits = c(0,100))

Residuals across the entire temporal extent of the dataset

# rasterize data
plotResid_rast <- pred_glm1 %>% 
         drop_na(resid) %>% 
  #slice_sample(n = 5e4) %>%
  terra::vect(geom = c("Long", "Lat")) %>% 
  terra::set.crs(crs(test_rast)) %>% 
  terra::rasterize(y = test_rast, 
                   field = "resid", 
                   fun = mean) #%>% 
  #terra::aggregate(fact = 2, fun = mean, na.rm = TRUE) %>% 
  #terra::crop(ext(-1950000, 1000000, -1800000, 1000000))

# get the extent of this particular raster, and crop it accordingly
tempExt <- crds(plotResid_rast, na.rm = TRUE)

plotResid_rast_2 <- plotResid_rast %>% 
  crop(ext(min(tempExt[,1]), max(tempExt[,1]),
           min(tempExt[,2]), max(tempExt[,2])) 
       )

# identify locations where residuals are >100 or < -100
badResids_high <- pred_glm1 %>% 
  filter(resid > 100)  %>% 
  terra::vect(geom = c("Long", "Lat")) %>% 
  terra::set.crs(crs(test_rast)) 
badResids_low <- pred_glm1 %>% 
  filter(resid < -100)  %>% 
  terra::vect(geom = c("Long", "Lat")) %>% 
  terra::set.crs(crs(test_rast)) 
# make figures
map <- ggplot() +
geom_spatraster(data = 
plotResid_rast_2) + 
  geom_sf(data=cropped_states %>% st_transform(crs = st_crs(test_rast)) %>% st_crop(st_bbox(plotObs_2)),fill=NA )  + 
  geom_sf(data = badResids_high, col = "blue") +
  geom_sf(data = badResids_low, col = "red") +
labs(title = paste0("Resids. (obs. - pred.) from Grass/shrub ecoregion-wide model of ", response),
     subtitle = "bestLambda model \n red points indication locations that have residuals below -100 \n blue points indicate locatiosn that have residuals above 100") +
  scale_fill_gradient2(low = "red",
                       mid = "white" ,
                       high = "blue" , 
                       midpoint = 0,   na.value = "lightgrey",
                       limits = c(-100,100)
                       )
hist <- ggplot(pred_glm1) + 
  geom_histogram(aes(resid), fill = "lightgrey", col = "darkgrey") + 
  geom_text(aes(x = min(resid)*.9, y = 1500, label = paste0("min = ", round(min(resid),2)))) +
  geom_text(aes(x = max(resid)*.9, y = 1500, label = paste0("max = ", round(max(resid),2))))

library(ggpubr)
ggarrange(map, hist, heights = c(3,1), ncol = 1)

Quantile plots

Binning predictor variables into “Deciles” (actually percentiles) and looking at the mean predicted probability for each percentile. The use of the word Decentiles is just a legacy thing (they started out being actual Percentiles)

var_prop_pred <- paste0(response, "_pred")
response_vars <- c(response, var_prop_pred)

prednames_fig <- paste(str_split(globModTerms, ":", simplify = TRUE)) 
prednames_fig <- str_replace(prednames_fig, "I\\(", "")
prednames_fig <- str_replace(prednames_fig, "\\^2\\)", "")
prednames_fig <- unique(prednames_fig[prednames_fig>0])
if (length(prednames_fig) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
  pred_glm1_deciles <- predvars2deciles(pred_glm1,
                                      response_vars = response_vars,
                                        pred_vars = prednames_fig)
}

Here is a quick version of LOESS curves fit to raw data (to double-check the quantile plot calculations)

if (length(prednames_fig) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
  pred_glm1 %>%
  select(all_of(c(prednames_fig, response_vars))) %>%
  pivot_longer(cols = prednames_fig)  %>%
  ggplot() +
  facet_wrap(~name, scales = "free") +
  geom_point(aes(x = value, y =  .data[[paste(response)]]), col = "darkblue", alpha = .1)  + # observed values
  geom_point(aes(x = value, y = .data[[response_vars[2]]]), col = "lightblue", alpha = .1) + # model-predicted values
  geom_smooth(aes(x = value, y =  .data[[paste(response)]]), col = "black", se = FALSE) +
  geom_smooth(aes(x = value, y = .data[[response_vars[2]]]), col = "brown", se = FALSE)

}

Below are the actual quantile plots (note that the predictor variables are scaled)

if (length(prednames_fig) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {

# publication quality version
g3 <- decile_dotplot_pq(pred_glm1_deciles, response = response) + ggtitle("Decile Plot")

g4 <- add_dotplot_inset(g3, pred_glm1_deciles)


  
if(save_figs) {
  png(paste0("figures/quantile_plots/quantile_plot_", response,  "_",ecoregion,".png"), 
     units = "in", res = 600, width = 5.5, height = 3.5 )
    print(g4)
  dev.off()
}

g4
}

Deciles Filtered

20th and 80th percentiles for each climate variable

df <- pred_glm1[, prednames_fig] #%>% 
  #mutate(MAT = MAT - 273.15) # k to c
quantiles <- map(df, quantile, probs = c(0.2, 0.8), na.rm = TRUE)

Filtered ‘Decile’ plots of data. These plots show each vegetation variable, but only based on data that falls into the upper and lower two deciles of each predictor variable.

if (length(prednames_fig) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
pred_glm1_deciles_filt <- predvars2deciles( pred_glm1, 
                         response_vars = response_vars,
                         pred_vars = prednames_fig,
                         filter_var = TRUE,
                         filter_vars = prednames_fig) 

decile_dotplot_filtered_pq(pred_glm1_deciles_filt, xvars = prednames_fig)
#decile_dotplot_filtered_pq(pred_glm1_deciles_filt)

}

Filtered quantile figure with middle 2 deciles also shown

if (length(prednames_fig) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
pred_glm1_deciles_filt_mid <- predvars2deciles(pred_glm1, 
                         response_vars = response_vars,
                         pred_vars = prednames_fig,
                         filter_vars = prednames_fig,
                         filter_var = TRUE,
                         add_mid = TRUE)

g <- decile_dotplot_filtered_pq(df = pred_glm1_deciles_filt_mid, xvars = prednames_fig)
g

if(save_figs) {x
jpeg(paste0("figures/quantile_plots/quantile_plot_filtered_mid_v1", , ".jpeg"),
     units = "in", res = 600, width = 5.5, height = 6 )
  g 
dev.off()
}
}

Cross-validation

Use terms from global model to re-fit and predict on different held out regions

Figures show residuals for each of the models fit to held-out ecoregions

These models were fit to six ecoregions, and then predict on the indicated heldout ecoregion

if (length(prednames_fig) == 0) {
  print("The model only contains one predictor (an intercept), so cross validation isn't practical")
} else {



## code from Tredennick et al. 2020
# try each separate level II ecoregion as a test set
# make a list to hold output data
outList <- vector(mode = "list", length = length(sort(unique(modDat_1$NA_L2NAME))))
# obs_pred <- data.frame(ecoregion = character(),obs = numeric(),
#                        pred_opt = numeric(), pred_null = numeric()#,
#                        #pred_nopenalty = numeric()
#                        )

## get the model specification from the global model
mat <- as.matrix(coef(fit_glm_bestLambda, s = "lambda.min"))
mat2 <- mat[mat[,1] != 0,]

f_cv <- as.formula(paste0(response, " ~ ", paste0(names(mat2)[2:length(names(mat2))], collapse = " + ")))

X_cv <- model.matrix(object = f_cv, data = modDat_1_s)
# get response variable
y_cv <- as.matrix(modDat_1_s[,response])

  
# now, loop through so with each iteration, a different ecoregion is held out
 for(i_eco in sort(unique(modDat_1_s$NA_L2NAME))){

  # split into training and test sets
  test_eco <- i_eco
  print(test_eco)
  # identify the rowID of observations to be in the training and test datasets
  train <- which(modDat_1_s$NA_L2NAME!=test_eco) # data for all ecoregions that aren't 'i_eco'
  test <- which(modDat_1_s$NA_L2NAME==test_eco) # data for the ecoregion that is 'i_eco'

  trainDat_all <- modDat_1_s %>% 
    slice(train) %>% 
    select(-newRegion)
  testDat_all <- modDat_1_s %>% 
    slice(test) %>% 
    select(-newRegion)

  # get the model matrices for input and response variables for cross validation model specification
  X_train <- as.matrix(X_cv[train,])
  X_test <- as.matrix(X_cv[test,])

  y_train <- modDat_1_s[train,response]
  y_test <- modDat_1_s[test,response]
  
  # get the model matrices for input and response variables for original model specification
  X_train_glob <- as.matrix(X[train,])
  X_test_glob <- as.matrix(X[test,])

  y_train_glob <- modDat_1_s[train,response]
  y_test_glob <- modDat_1_s[test,response]

  train_eco <- modDat_1_s$NA_L2NAME[train]

  # Fit model using glm-----------------------------------------------
#
#   # specify leave-one-year-out cross-validation
#   my_folds <- as.numeric(as.factor(train_eco))
#
  # fit_i <- glmnet(
  #   x = X_train[,2:ncol(X_train)],
  #   y = y_train,
  #   #family = gaussian,
  #   family = stats::Gamma(link = "log"),
  #   alpha = 1,  # 0 == ridge regression, 1 == lasso, 0.5 ~~ elastic net
  #   #lambda = lambdas,
  #   #type.measure="mse",
  #   #penalty.factor = pen_facts,
  #   foldid = my_folds,
  #   standardize = TRUE
  # )

  ## just try a regular glm w/ the components from the global model
  fit_i <- glm(data = trainDat_all, formula = f_cv, 
    # data = trainDat_all, 
    # formula = TotalTreeCover ~ prcp_s + prcp_seasonality_s + prcpTempCorr_s + 
    # carbon_s + AWHC_s + t_warm_anom_s + prcp_wet_anom_s + annWetDegDays_anom_s +
    # VPD_min_anom_s + I(prcp_seasonality_s^2) + I(prcpTempCorr_s^2) +
    # I(isothermality_s^2) + I(annWatDef_s^2) + I(tmin_anom_s^2) +
    # I(precp_dry_anom_s^2) + I(prcpTempCorr_anom_s^2) + I(annWatDef_anom_s^2) +
    # I(VPD_min_anom_s^2) + I(sand_s^2) + I(AWHC_s^2) + annWatDef_s:annWetDegDays_anom_s +
    # prcpTempCorr_s:annWatDef_s + prcp_seasonality_anom_s:annWetDegDays_anom_s +
    # prcpTempCorr_anom_s:annWetDegDays_anom_s + prcpTempCorr_s:annWetDegDays_anom_s +
    # tmean_s:frostFreeDays_5_anom_s + prcp_s:isothermality_s +
    # t_warm_anom_s:prcp_seasonality_anom_s + tmin_anom_s:t_warm_anom_s +
    # sand_s:AWHC_s
    ,
               family =  stats::Gamma(link = "log")
    )

    coef(fit_i)
    
  # lasso model predictions with the optimal lambda
  optimal_pred <- predict(fit_i, newdata= testDat_all, type = "response"
                          )
  # null model and predictions
  # the "null" model in this case is the global model
  # predict on the test data for this iteration w/ the global model 
  null_pred <- predict.glm(fit_glm_bestLambda, newdata = testDat_all, type = "response")

  # save data
  tmp <- data.frame(ecoRegion_holdout = rep(test_eco,length(y_test)),obs=y_test,
                    pred_opt=optimal_pred, pred_null=null_pred#,
                    #pred_nopenalty=nopen_pred
                    ) %>%
    cbind(testDat_all)
  # put output into a list
  tmpList <- list("testRegion" = i_eco,
    "modelObject" = fit_i,
       "modelPredictions" = tmp)

  # save model outputs
  outList[[which(sort(unique(modDat_1_s$NA_L2NAME)) == i_eco)]] <- tmpList
  # save one example of model fits
  # if(i_eco==sort(unique(modDat_1_s$NA_L2NAME))[1]){
  #   # save model object
  #   saveRDS(fit,file="./ModelResults/glmnet_fit.RDS")
  #
  #   #saveRDS(nopen,file="./ModelResults/nopenalty_fit.RDS")
  # }
 }

#
# # calculate correlations between null and optimal model
# my_cors <- c(cor(outList[[i]]$modelPredictions$pred_opt, outList[[i]]$modelPredictions$obs), # correlation of LOO model's predictions w/ the observations
#             cor(outList[[i]]$modelPredictions$s1, outList[[i]]$modelPredictions$obs)#, # correlations of LOO model's predictions w/ global model's predictions
#             #cor(obs_pred$pred_nopenalty,obs_pred$obs)
#             )
# 
# # calculate mse between null and optimal model
# my_mse <- c(mean((outList[[i]]$modelPredictions$pred_opt - outList[[i]]$modelPredictions$obs)^2) ,
#             mean((outList[[i]]$modelPredictions$s1 - outList[[i]]$modelPredictions$obs)^2)#,
#             #mean((obs_pred$pred_nopenalty - obs_pred$obs)^2)
#             )

# # print results
# names(my_cors) <- names(my_mse) <- c("optimal","null"#,"no penalty"
#                                      )
# print(my_cors)
# print(my_mse)
#
# # save obs vs pred results
# write.csv(obs_pred,"./ModelResults/obs_vs_pred.csv",row.names=F)

for (i in 1:length(unique(modDat_1_s$NA_L2NAME))) {
  holdoutRegion <- outList[[i]]$testRegion
  predictionData <- outList[[i]]$modelPredictions
  modTerms <- as.matrix(coef(outList[[i]]$modelObject)) %>%
    as.data.frame() %>%
    filter(V1!=0) %>%
    rownames()

  # calculate residuals
  predictionData <- predictionData %>%
  mutate(resid = .[["obs"]] - .[["pred_opt"]] ,
         resid_globMod = .[["obs"]]  - .[["pred_null"]])


# rasterize
# use 'test_rast' from earlier

  # rasterize data
plotObs <- predictionData %>%
         drop_na(paste(response)) %>%
  #slice_sample(n = 5e4) %>%
  terra::vect(geom = c("Long", "Lat")) %>%
  terra::set.crs(crs(test_rast)) %>%
  terra::rasterize(y = test_rast,
                   field = "resid",
                   fun = mean) #%>%
  #terra::aggregate(fact = 2, fun = mean, na.rm = TRUE) %>%
  #terra::crop(ext(-1950000, 1000000, -1800000, 1000000))

tempExt <- crds(plotObs, na.rm = TRUE)

plotObs_2 <- plotObs %>% 
  crop(ext(min(tempExt[,1]), max(tempExt[,1]),
           min(tempExt[,2]), max(tempExt[,2])) 
       )

# identify locations where residuals are >100 or < -100
badResids_high <- predictionData %>% 
  filter(resid > 100)  %>% 
  terra::vect(geom = c("Long", "Lat")) %>% 
  terra::set.crs(crs(test_rast)) 
badResids_low <- predictionData %>% 
  filter(resid < -100)  %>% 
  terra::vect(geom = c("Long", "Lat")) %>% 
  terra::set.crs(crs(test_rast)) 


# make figures
# make histogram
hist_i <- ggplot(predictionData) +
  geom_histogram(aes(resid_globMod), col = "darkgrey", fill = "lightgrey") +
  xlab(c("Residuals (obs. - pred.)"))
# make map
map_i <-  ggplot() +
geom_spatraster(data = plotObs_2) +
  geom_sf(data=cropped_states %>% st_transform(crs = st_crs(test_rast)) %>% st_crop(st_bbox(plotObs_2)),fill=NA ) +
  geom_sf(data = badResids_high, col = "blue") +
  geom_sf(data = badResids_low, col = "red") +
labs(title = paste0("Residuals (obs. - pred.) for predictions of \n", holdoutRegion, " \n from a model fit to other ecoregions"),
     subtitle = paste0(response, " ~ ", paste0( modTerms, collapse = " + "))) +
  scale_fill_gradient2(low = "red",
                       mid = "white" ,
                       high = "blue" ,
                       midpoint = 0,   na.value = "lightgrey",
                       limits = c(-100, 100))

 assign(paste0("residPlot_",holdoutRegion),
   value = ggarrange(map_i, hist_i, heights = c(3,1), ncol = 1)
)

}


  lapply(unique(modDat_1_s$NA_L2NAME), FUN = function(x) {
    get(paste0("residPlot_", x))
  })
}
## [1] "COLD DESERTS"
## [1] "MEDITERRANEAN PIEDMONT"
## [1] "SEMIARID PLAIN AND PRAIRIES"
## [1] "TEMPERATE PRAIRIES"
## [1] "WARM DESERTS"
## [1] "WEST-CENTRAL SEMIARID PRAIRIES"
## [[1]]

## 
## [[2]]

## 
## [[3]]

## 
## [[4]]

## 
## [[5]]

## 
## [[6]]

Save output

# # glm models
# #mods2save <- butcher::butcher(mod_glmFinal) # removes some model components so the saved object isn't huge
# 
# #mods2save$formula <- best_form
# #mods2save$pred_vars_inter <- pred_vars_inter # so have interactions
# #n <- nrow(df_sample)
# #mods2save$data_rows <- n
# 
# 
# if(!test_run) {
#   saveRDS(mods2save, 
#         paste0("./models/glm_beta_model_CONUSwide_", s, "_n", n, 
#         #sample_group, 
#         ".RDS"))
#   if (byRegion == TRUE) {
#     ## western forests
#      saveRDS(mods2save_WF, 
#         paste0("./models/glm_beta_model_WesternForests_", s, "_n", n, 
#         #sample_group, 
#         ".RDS"))
#     ## eastern forests
#      saveRDS(mods2save_EF, 
#         paste0("./models/glm_beta_model_EasternForests_", s, "_n", n, 
#         #sample_group, 
#         ".RDS"))
#      ## grass/shrub
#      saveRDS(mods2save_G, 
#         paste0("./models/glm_beta_model_GrassShrub_", s, "_n", n, 
#         #sample_group, 
#         ".RDS"))
#   }
# }
## partial dependence plots
#vip::vip(mod_glmFinal, num_features = 15)

#pdp_all_vars(mod_glmFinal, mod_vars = pred_vars, ylab = 'probability',train = df_small)

#caret::varImp(fit)

session info

Hash of current commit (i.e. to ID the version of the code used)

system("git rev-parse HEAD", intern=TRUE)
## [1] "79890c55a196d40eb16ae968701c4515b44c260c"

Packages etc.

sessionInfo()
## R version 4.4.0 (2024-04-24)
## Platform: aarch64-apple-darwin20
## Running under: macOS Sonoma 14.6.1
## 
## Matrix products: default
## BLAS:   /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## time zone: America/Denver
## tzcode source: internal
## 
## attached base packages:
## [1] parallel  stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggpubr_0.6.0     doMC_1.3.8       iterators_1.0.14 foreach_1.5.2    factoextra_1.0.7 glmnet_4.1-8    
##  [7] Matrix_1.7-0     kableExtra_1.4.0 rsample_1.2.1    here_1.0.1       StepBeta_2.1.0   ggtext_0.1.2    
## [13] knitr_1.49       gridExtra_2.3    pdp_0.8.2        GGally_2.2.1     lubridate_1.9.4  forcats_1.0.0   
## [19] stringr_1.5.1    dplyr_1.1.4      purrr_1.0.4      readr_2.1.5      tidyr_1.3.1      tibble_3.2.1    
## [25] tidyverse_2.0.0  caret_6.0-94     lattice_0.22-6   ggplot2_3.5.1    sf_1.0-16        tidyterra_0.6.1 
## [31] terra_1.8-21     ggspatial_1.1.9  dtplyr_1.3.1     patchwork_1.3.0 
## 
## loaded via a namespace (and not attached):
##   [1] RColorBrewer_1.1-3   rstudioapi_0.17.1    jsonlite_1.9.1       shape_1.4.6.1        magrittr_2.0.3      
##   [6] modeltools_0.2-23    farver_2.1.2         rmarkdown_2.29       vctrs_0.6.5          rstatix_0.7.2       
##  [11] htmltools_0.5.8.1    curl_6.2.1           broom_1.0.7          Formula_1.2-5        pROC_1.18.5         
##  [16] sass_0.4.9           parallelly_1.37.1    KernSmooth_2.23-22   bslib_0.9.0          plyr_1.8.9          
##  [21] sandwich_3.1-0       zoo_1.8-12           cachem_1.1.0         uuid_1.2-1           commonmark_1.9.1    
##  [26] lifecycle_1.0.4      pkgconfig_2.0.3      R6_2.6.1             fastmap_1.2.0        future_1.33.2       
##  [31] digest_0.6.37        colorspace_2.1-1     furrr_0.3.1          rprojroot_2.0.4      pkgload_1.3.4       
##  [36] labeling_0.4.3       timechange_0.3.0     mgcv_1.9-1           httr_1.4.7           abind_1.4-8         
##  [41] compiler_4.4.0       proxy_0.4-27         aod_1.3.3            withr_3.0.2          backports_1.5.0     
##  [46] carData_3.0-5        betareg_3.1-4        DBI_1.2.3            ggstats_0.9.0        ggsignif_0.6.4      
##  [51] MASS_7.3-60.2        lava_1.8.0           rappdirs_0.3.3       classInt_0.4-10      gtools_3.9.5        
##  [56] ModelMetrics_1.2.2.2 tools_4.4.0          units_0.8-5          lmtest_0.9-40        future.apply_1.11.2 
##  [61] nnet_7.3-19          glue_1.8.0           nlme_3.1-164         gridtext_0.1.5       grid_4.4.0          
##  [66] reshape2_1.4.4       generics_0.1.3       recipes_1.1.0        gtable_0.3.6         tzdb_0.4.0          
##  [71] class_7.3-22         data.table_1.17.0    hms_1.1.3            utf8_1.2.4           xml2_1.3.7          
##  [76] car_3.1-2            flexmix_2.3-19       markdown_1.13        ggrepel_0.9.5        pillar_1.10.1       
##  [81] splines_4.4.0        survival_3.5-8       tidyselect_1.2.1     svglite_2.1.3        stats4_4.4.0        
##  [86] xfun_0.51            hardhat_1.4.0        timeDate_4032.109    stringi_1.8.4        yaml_2.3.10         
##  [91] evaluate_1.0.3       codetools_0.2-20     cli_3.6.4            rpart_4.1.23         systemfonts_1.2.1   
##  [96] munsell_0.5.1        jquerylib_0.1.4      Rcpp_1.0.14          globals_0.16.3       gower_1.0.1         
## [101] listenv_0.9.1        tigris_2.1           viridisLite_0.4.2    ipred_0.9-15         scales_1.3.0        
## [106] prodlim_2024.06.25   e1071_1.7-14         crayon_1.5.3         combinat_0.0-8       rlang_1.1.5         
## [111] cowplot_1.1.3